document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=800786>Question 800786</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For their field studies in marine ecology, a group of students rented a boat for P360. However, seven students had to withdraw from the group and as a result, the share of each of the remaining students was increased by P21.00. How many students were there in the original group? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #483286 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=483286\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For their field studies in marine ecology, a group of students rented a boat for P360. <BR>\n" );
document.write( "However, seven students had to withdraw from the group and as a result, the share of each of the remaining students was increased by P21.00.<BR>\n" );
document.write( " How many students were there in the original group?<BR>\n" );
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document.write( "Let x = no. of students in original group<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%2Fx ALIGN=MIDDLE  ALT=\"360%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = original price per students<BR>\n" );
document.write( "then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%2F%28%28x-7%29%29 ALIGN=MIDDLE  ALT=\"360%2F%28%28x-7%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = actual price per student<BR>\n" );
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document.write( "Actual price - original price = 21<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%2F%28%28x-7%29%29 ALIGN=MIDDLE  ALT=\"360%2F%28%28x-7%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%2Fx ALIGN=MIDDLE  ALT=\"360%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 21<BR>\n" );
document.write( "multiply by x(x-7) to clear the denominators, resulting in:<BR>\n" );
document.write( "360x - 360(x-7) = 21x(x-7)<BR>\n" );
document.write( "360x - 360x + 2520 = 21x^2 - 147x<BR>\n" );
document.write( "Combine as a quadratic equation<BR>\n" );
document.write( "0 = 21x^2 - 147x - 2520<BR>\n" );
document.write( "simplify, divide by 21<BR>\n" );
document.write( "x^2 - 7x - 120 = 0<BR>\n" );
document.write( "Factors to <BR>\n" );
document.write( "(x-15) (x+8) = 0<BR>\n" );
document.write( "the positive solution is all we want here<BR>\n" );
document.write( "x = 15 students originally<BR>\n" );
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document.write( "See if that checks out, find the cost per student<BR>\n" );
document.write( "360/8 = 45 (actual)<BR>\n" );
document.write( "360/15= 24 (originally)<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "diff: 21 </SPAN>\n" );
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